CHANGING RWYS AND DEP PROCS AT DCA; D328 FLT CREW MISS CORRECT DEP FREQ AND XPONDER SETTING ON TKOF.

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TAXIING FOR TKOF; OUR DEP RWY WAS CHANGED TWICE FOR VARIOUS REASONS. UPON TALKING ABOUT THE DEP; I TOLD THE CAPT (THE PNF) THAT I WOULD VERIFY WITH TWR BEFORE TKOF WHAT THE APPROPRIATE DEP FREQ WOULD NOW BE. WE WERE CLRED INTO POS AND HOLD. THE CAPT THEN GAVE ME THE CTLS WHICH IS NOT OUR NORMAL PROC BEFORE RECEIVING TKOF CLRNC. HE DID IT BECAUSE WE KNEW THAT AN 'IMMEDIATE' DEP WOULD BE FORTHCOMING. HE NOW HAD THE RADIOS. WHEN SUBSEQUENTLY CLRED FOR TKOF; WE WERE TOLD TO EXPEDITE AND GIVEN AN UNUSUAL CLRNC TO TURN TO A 090 DEG HDG UPON DEP FROM RWY 1. GND HAD PREVIOUSLY TOLD US TO TRACK OUTBOUND ON THE DCA 328 DEG RADIAL; AN USUAL CLRNC. THE CEILINGS WERE LOW AND THERE WOULD BE NO WAY OF ENSURING THAT WE COULD REMAIN CLR OF THE VERY SENSITIVE PROHIBITED AREAS IN THE AREA. WE; THEREFORE; APPROPRIATELY QUESTIONED THE CLRNC AND THE CTLR CHANGED IT BACK TO THE 328 DEG RADIAL; THOUGH HE WAS OBVIOUSLY UPSET BECAUSE THIS EXCHANGE WAS UNEXPECTED CONSIDERING HIS INSTRUCTION TO EXPEDITE. WE TOOK OFF; AND THE ACFT ON ARR DID NOT HAVE TO GO AROUND. UPON CONTACTING DEP; THE CTLR WAS AT FIRST SILENT THEN OBVIOUSLY UPSET WITH US. SHE TOLD US THAT WE WERE BOTH ON THE WRONG FREQ (THE CAPT HAD FORGOTTEN TO VERIFY THE FREQ DUE TO THE ABNORMAL TKOF SIT); AND THAT WE WERE ON THE WRONG SQUAWK CODE. AGAIN; NOT A GOOD THING IN THIS SENSITIVE AIRSPACE. THE CAPT WHO HAD SET UP THE RADIOS HAD READ HIS OWN WRITING INCORRECTLY AND ENTERED THE WRONG SQUAWK CODE. WHEN I HAD READ HIS WRITING ON THE GND; IT APPEARED THE SAME AS WHAT HE HAD ENTERED IN THE XPONDER. ALL THE XCHKS IN THE WORLD CANNOT HELP ILLEGIBLE WRITING.